Fill along the front of a path of an SVG
Don't needlessly convert your bezier to a mesh unless strictly necessary, it is a destructive process and will ruin your model and the benefits of using curve objects.

For an animated outline and fill effect you will need to independent copies of your original SVG imported curve object.

Animated Outline

For the animated outline make sure a new copy of your original curve is set to 2D, non-cyclic (i.e. open) and has no fill. Then add a Bevel Width to it as desired then animate the Bevel Factor Start or Bevel Factor End property by keyframing it.



Animated Fill

For the fill animation a new independent copy of the original curve is needed. Extrude it and bevel it as desired, by using the builtin Curve Extrude and Bevel properties.

Afterwards add a Build Modifier to it, and adjust the animation parameters as desired. You can see the result by scrubbing the time line.



To animate fill followed by extrusion afterwards, keyframe the "fill process" of the Build modifier so it starts and ends first, then animate the Extrude parameter of the curve by keyframing it, so it only starts after the build concludes